Consistent and accurate methods for performing state estimation in a wide-variety of systems are critical to the function of many processes and operations, both civilian and military. Systems and methods have been developed for state estimation of a system that may transition between different regimes of operation (e.g., flight regimes) which may be described or defined by a plurality of discrete models. These state estimation methods may be applied to various systems having sensory inputs, by way of non-limiting example only, nuclear, chemical, or manufacturing factories or facilities, control processes subject to external parameter changes, space stations subject to vibrations, automobiles subject to road conditions, and the like. One particularly useful application for state estimation is tracking objects in flight, such as a multistage rocket that is transitioning back and forth between a ballistic model of flight and thrust modes, or an aircraft performing maneuvers mid-flight. For example, an aircraft being tracked may engage in multiple different regimes such as such as cruise, loiter, supersonic dash, maneuvers such as pop-up maneuvers, and missile launch. Likewise, a multistage rocket may engage in different regimes such as ballistic flight and boosted or propelled flight.
Recent state estimate systems include Optimal Reduced State Estimation (ORSE) filters for tracking an object. ORSE filters are reduced state because parametric acceleration is not represented in the filter model but is instead estimated as an independently calculated part of the covariance matrix. The filter is optimal because it reduces errors in the least squares sense. ORSE filters include bounds or maximum excursions for various parameters, and minimizes the mean-square and, thus, the root-mean-square (RMS) estimation errors for the maximum excursions of the parameters in the truth model. Furthermore, because the bounds are included in the minimized covariance, embodiments of the present invention do not need white plant noise, as is required by Kalman filters, to cope with the reduced state. In an exemplary aircraft tracking embodiment, using the physical bounds (i.e. maximum excursions) on various parameters, such as turn rate boundary parameters and tangential acceleration boundary parameters, ORSE filtering may provide for increased estimation consistency. Maximum accelerations produced by these bounded parameters, along the instantaneous normal and tangential airplane axes, bound all physically possible maneuvers. U.S. Pat. No. 7,180,443, issued Feb. 20, 2007 in the names of Mookerjee and Reifler, which is incorporated by reference in its entirety, describes an ORSE state estimator for determining state estimation and state error covariances for generalized or arbitrary motion of a target or moving object where the sensors provide complete measurements, namely each measurement locating a point in three dimensional space at a known time with a non-singular measurement covariance matrix.
Current implementations of ORSE initialize various parameters with the maximum bias or excursions expected over the lifetime of the track. However, maximum bias input into an ORSE filter may be unnecessarily oversized and may become stale over time. Thus, the current initialization implementations cause oversized uncertainties, in particular when maximum bias/uncompensated acceleration is dependent upon current track state. An example are drag forces, which vary with speed and altitude. In current implementations, the ORSE component for drag is initialized as the highest drag expected over the duration of the track, which may overestimate the magnitude of drag over much of the trajectory. For example, current ORSE implementation may use a lambda matrix containing the maximum expected uncompensated acceleration. When representing drag and similar forces that depend upon flight regime, the initial selection may no longer be applicable and potentially assume maximum accelerations far higher than may be possible.
Improved systems and methods for ORSE state estimation are desired.